Comparing Meta-analysis and Individual Person Data Analysis Using Raw Data on Children's Understanding of Equivalence.

A prevailing theory of mathematical problem solving predicts that children will be less accurate solving a + b = c + __ problems versus a + b = __ + c. However, this has never been tested directly. Because of low base rates, information combined from multiple studies can help improve estimation accuracy and precision. This study compared meta-analysis and individual person data (IPD) analysis using raw data from 14 studies (N = 1,414; ns = 30-232; Mage reported = 8;7). Substantive results challenge the prevailing theory. Methodological results demonstrate the advantages of using meta-analysis and IPD over single-study analysis. Moreover, IPD can be more powerful than meta-regression for detecting between-study moderation effects.